With the advent of inexpensive digital color printers, methods and systems of color digital halftoning have become increasingly important in the reproduction of printed or displayed images possessing continuous color tones. It is well understood that most digital color printers operate in a binary mode, i.e., for each color separation, a corresponding colorant spot is either printed or not printed at a specified location or pixel. Digital halftoning controls the printing of colorant spots, where the spatial averaging of the printed colorant spots by either a human visual system or a viewing instrument, provides the illusion of the required continuous color tones. In the art of printing, the color tone that results from the overlay of the halftone spots from multiple colorants is often referred to as “process color.” Color separations can be thought of as multiple channels that can be used to define the color of an image. Color separations are sometimes called colorant separations because they are used to specify amounts of colorants required to achieve a target perception of color.
The most common halftone technique is screening, which compares the required continuous tone colorant level of each pixel for each color separation with one or more predetermined threshold levels. The predetermined threshold levels are typically defined for a rectangular cell that is tiled to fill the plane of an image, thereby forming a halftone screen of threshold values. At a given pixel if the required continuous tone colorant level is darker than the threshold halftone level, a colorant spot is printed at that specified pixel. Otherwise the colorant spot is not printed. The output of the screening process is a binary pattern of multiple small “dots”, which are regularly spaced as is determined by the size, shape, and tiling of the halftone cell. In other words, the screening output halftone image separation, as a two-dimensionally repeated pattern, possesses two fundamental spatial frequencies, which are completely defined by the geometry of the halftone screen.
It is understood in the art that the distribution of printed pixels in a color halftone image separation depends on the design of the halftone screen. For clustered-dot halftone screens, all printed pixels formed using a single halftone cell typically group into one or more clusters. If a halftone cell only generates a single cluster, it is referred to as a single-dot halftone or single-dot halftone screen. Alternatively, halftone screens may be dual-dot, tri-dot, quad-dot, or the like.
While halftoning is often described in terms of halftone dots, it should be appreciated that idealized halftone dots can possess a variety of shapes that include rectangles, squares, lines, circles, ellipses, “plus signs”, X-shapes, pinwheels, and pincushions, and actual printed dots can possess distortions and fragmentation of those idealized shapes introduced by digitization and the physical printing process. Various digital halftone screens having different shapes and angles are described in “An Optimum Algorithm for Halftone Generation for Displays and Hard Copies”, by T. M. Holladay, Proc. Soc. for Information Display, 21, p. 185, 1980.
A common problem that arises in digital color halftoning is the manifestation of moiré patterns. Moiré patterns are undesirable interference patterns that occur when two or more color halftone image separations are printed over each other. Since color mixing during the printing process is a non-linear process, frequency components other than the fundamental frequencies and harmonics of the individual color halftone image separations can occur in the final printout. For example, if an identical halftone screen is used for two color image separations, theoretically, there should be no moiré patterns. However, any slight misalignment between the two color halftone image separations occurring from an angular difference and/or a scalar difference will result in two slightly different fundamental frequency vectors. Due to nonlinear color mixing the difference in frequency vectors produces a beat frequency which will be visibly evident as a very pronounced moiré interference pattern in the output. Additionally, lateral displacement misregistration can result in significant color shifts if an identical halftone screen is used for two color image separations. To avoid, for example, two-color moiré patterns and other color shifts due to misalignment and misregistration, or for other reasons, different halftone screens are commonly used for different color image separations, where the fundamental frequency vectors of the different halftone screens are separated by relatively large angles. Therefore, the frequency difference between any two fundamental frequencies of the different screens will be large enough so that no visibly objectionable moiré patterns are produced.
In selecting different halftone screens, for example for three color image separations, it is desirable to avoid any two-color moiré as well as any three-color moiré. It is well known that in the traditional printing industry that three halftone screens, which can be constructed by halftone cells that are square in shape and identical, can be placed at 15°, 45°, and 75°, respectively, from a point and axis of origin, to provide the classical three-color moiré-free solution. This is described in “Principles of Color Reproduction”, by J. A. G. Yule, John Wiley & Sons, N.Y., 1967.
However, for digital halftoning, the freedom to select a rotation of a halftone screen is limited by the raster structure, which defines the position of each pixel. Since tan (15°) and tan (75°) are irrational numbers, a halftone screen at a rotation of 15° or 75° cannot be implemented exactly in digital halftoning. To this end, some methods have been proposed to provide approximate instead of exact moiré-free solutions. For example, in U.S. Pat. No. 4,916,545, moiré is suppressed by randomly varying the dot fonts that are used to write successive halftone dots in the screened image. In U.S. Pat. No. 5,442,461, strips of a rational angled screen are concatenated to approximate an irrational angled screen. Errors which accumulate with each successive pixel are corrected by occasionally jumping to a new point in the strip. However, all these approximate solutions result in some halftone dots having centers that do not lie directly on addressable points, or on the pixel positions defined by the raster structure. Therefore, the shape and center location varies from one halftone dot to another. Consequently, additional interference or moiré between the screen frequencies and the raster frequency can occur. In another approach, U.S. Pat. No. 5,371,612 discloses a moiré prevention method to determine screen angles and sizes that is usable solely for square-shaped, halftone screens.
U.S. Pat. No. 5,155,599 to Delabastita discloses a screening system and method for reproduction of images in printing. The screening angles that are used are close, but not identical to conventional screening angles. The reproduction is nevertheless Moiré free by the fact that the deviations in angles from the conventional system are exactly offset by the deviations in line rulings. The screening system is particularly advantageous when used for combinations of screens with rational tangent angles. The Moiré free combination of rational tangent screens can be rotated by a constant angle with the amount of rotation controlled in small increments.
U.S. Pat. No. 6,798,539 to Wang et al., discloses methods for using single-cell, non-orthogonal clustered-dot screens to satisfy the moiré-free conditions for color halftoning. The disclosure also provides methods that combine single-cell non-orthogonal clustered-dot screens and line screens for moiré-free color halftoning. Particularly, the selection of these single-cell halftone screens is determined by satisfying moiré-free conditions provided in the respective spatial or frequency equations.
The difficulty in avoiding moiré between halftone screens is further exacerbated by the common practice of printing four colors. Four-color printing typically employs halftoning methods for the yellow image separation that produce less than optimal image quality. Typical clustered-dot methods often possess some residual moiré. The typical clustered-dot yellow configuration assumes square halftone cells and places yellow at 0° with a frequency that is ≈10% higher than the other screens. Low contrast moiré can be seen in many printed images for certain combinations of yellow and other colorants. Another common configuration for yellow utilizes a stochastic screen or error diffusion for yellow. That configuration results in a high degree of instability when used on many different printers. The result is inconsistency of color page-to-page and non-uniformity of color within a page.
There are several high quality printing applications that require more than four image separations. For example, high fidelity (“hi-fi”) color printing typically utilizes one or more additional primary colors as colorants to extend the gamut of a print engine. Two common choices of additional primaries are orange and green, but other colors, such as red, blue and violet may be used. A well known example of high fidelity printing is Pantone Hexachrome® printing. Low chroma printing employs an additional toner or ink with the same or similar hue as a conventional toner. For example, low chroma magenta may be used along with conventional magenta to enable smoother tone gradations and reduced texture in flesh tones compared to using conventional magenta alone. Typical low chroma, or light, colorants include light magenta, light cyan, and gray. Dark yellow is also used as a low chroma colorant. Other printing methods including more than four colorants may employ special colorants such as white, metallics and fluorescents, and may have applications in security and special imaging effects.
Due to moiré considerations associated with additional clustered-dot halftone screens, the alternatives currently available for fifth channel (separation) halftoning suffer from instability, less than desirable halftone structure appearance, or limitations on applications. For example, stochastic screens and error diffusion have been used for hi-fi color and low chroma toners, but the small dot sizes tend to produce unstable results for xerography and offset printing. Line screens have also been used, but the line structure tends to be considered undesirable unless used at very high frequencies, which can be unstable. Some methods utilize the same screen for a hi-fi colorant and for its complimentary colorant (e.g., same screen for cyan and orange), but that method can place limitations on the color management operations and does not apply to low chroma toners.
U.S. Pat. No. 5,870,530 to Balasubramanian discloses a “hi-fi” color printing system, wherein colorants of secondary colors beyond the regular CMYK (cyan, magenta, yellow, black) primary colorants are available, and the colorants of the secondary colors are substituted for combinations of the primary colorants in order to obtain a full color gamut. The functions by which colorants of the secondary colors are substituted for primary colorant are non-linear through a path in the color space.
U.S. Pat. No. 5,892,891 to Dalal et al. discloses a “hi-fi” color printing system, wherein colorants of hi-fi colors beyond the regular CMYK primary colorants are available, a main gamut obtainable with the CMYK colorants only is mutually exclusive with at least one extended gamut in which a hi-fi colorant is used and a complementary one of the CMY colorants is excluded. Because the main and extended gamuts are mutually exclusive, no more than four colorants are used in any part of the image, and no more than four halftone screens need be used to obtain any desired color.
The above indicated patents and citations provide a background basis for the disclosure as taught in the specification which follows below, and further for each of the patents and citations above, the disclosures therein are totally incorporated herein by reference in their entirety for their teachings.
As provided herein, there are supplied teachings to systems and methods that utilize three or four rotated hexagonal screens, or more precisely, screens that generate hexagonally tiled clusters, for moiré-free color printing